Inventiones mathematicae

, Volume 115, Issue 1, pp 435–462

Non-optimal levels of modl modular representations

  • Fred Diamond
  • Richard Taylor
Article

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [AL] Atkin, A. Li, W.: Twists of newforms and pseudo-eigenvalues ofW-operators. Invent. Math.48, 221–243 (1978)Google Scholar
  2. [BJ] Borel, A. Jacquet, H.: Automorphic forms and automorphic representations. In: Borel, A., Casselman, W. (eds.) Automorphic forms, representations and L-functions. Proc. Symp. Pure Math. vol. 33, part 1, pp 189–202) Providence, RI: Am. Math. Soc. 1979Google Scholar
  3. [B] Boutot, J.-F.: Variétés de Shimura: Le problème de modules en inégale caractéristique. Publ. Math. Univ. Paris, VII6, 43–62 (1979)Google Scholar
  4. [BC] Boutot, J.-F., Carayol, H.: Uniformisation p-adiques des courbes de Shimura; les théorèmes de Čerednik et Drinfeld. Astérisque196–197, 45–159 (1991)Google Scholar
  5. [C] Carayol, H.: Sur les représentations Galoisiennes modulol attachées aux formes modulaires. Duke Math. J.59, 785–801 (1989)Google Scholar
  6. [De] Deligne, P. Travaux de Shimura. In: Sémin. Bourbaki exposi 389 (1970–1971). In: Lect. Notes Math., vol. 244, pp. 123–165. Berlin, Heidelberg New York Springer 1971Google Scholar
  7. [DR] Deligne, P., Rapoport, M.: Les schémas de modules de courbes elliptiques. In: Deligne, P., Kuyk, W. (eds.) Modular functions of one variable II. (Lect. Notes Math., vol. 349, pp. 143–316) Berlin Heidelberg New York: Springer 1973Google Scholar
  8. [Di] Diamond, F.: Congruence primes for cusp forms of weightk≧2. Astérisque196–197 202–215 (1991)Google Scholar
  9. [F] Faltings, G.: Crystalline cohomology and p-adic Galois representations. In: Algebraic Analysis, Geometry and Number Theory. Proc. JAMI Inaugural Conference, pp. 25–79. Baltimore: Johns-Hopkins University Press 1989Google Scholar
  10. [FC] Faltings, G. Chai, C.-L.: Degeneration of abelian varieties. (Ergeb. Math. Grenzgeb. 3. Folge, Bd. 22) Berlin Heidelberg New York: Springer 1990Google Scholar
  11. [FJ] Faltings, G., Jordan, B.: Crystalline cohomology and GL(2, ℚ). (Preprint)Google Scholar
  12. [FL] Fontaine, J.-M., Lafaille, G.: Construction de représentations p-adiques. Ann. Sci. Ec. Norm. Supér.15, 547–608 (1982)Google Scholar
  13. [FM] Fontaine, J.-M., Messing, W.: p-adic periods and p-adic etale cohomology. Contemp. Math.67, 179–207 (1987)Google Scholar
  14. [G] Gelbart, S.: Automorphic forms on adele groups. (Ann. Math. Stud., 83) vol. Princeton: Princeton University Press 1975Google Scholar
  15. [H] Huppert, B.: Endliche Gruppen I. Grundlehren Math. Wiss., Bol. 134) Berlin Heidelberg New York: Springer 1983Google Scholar
  16. [Hi] Hida, H.: On p-adic Hecke algebras for GL2 over totally real fields. Ann. Math.128, 295–384 (1988)Google Scholar
  17. [JaLa] Jacquet, H., Langlands, R.: Automorphic forms on GL2 (Lect. Notes Math., vol. Berlin Heidelberg New York. Springer 1970Google Scholar
  18. [JoLi] Jordan, B., Livné, R.: Conjecture “Epsilon” for weightk>2. Bull. Am. Math. Soc.21, 51–56 (1989)Google Scholar
  19. [L] Livné, R.: On the conductors of moll representations coming from modular forms. Number Theory31, 133–141 (1989)Google Scholar
  20. [M] Mumford, D.: Abelian varieties. Oxford: University Press 1970Google Scholar
  21. [R1] Ribet, K.: Congruence relations between modular forms. In: Ciesielski, Z., Olech, C. (eds.) Proc. Int. Cong. of Mathematicians 1983, pp. 503–514. Warsaw: PWN 1984Google Scholar
  22. [R2] Ribet, K.: On modular representations of 462-2 arising from modular forms. Invent. Math.100, 431–476 (1990)Google Scholar
  23. [R3] Ribet, K.: Report on modl representations of Gal(ℚ/ℚ) arising from modular forms. In: Proc. of the motives conference, Seattle 1991, (to appear)Google Scholar
  24. [S1] Serre, J-P.: Arbres, amalgames, SL2. Astérisque46 (1977)Google Scholar
  25. [S2] Serre, J-P.: Sur les représentations modulaires de degré 2 de 462-4. Duke Math. J.54, 179–230 (1987)Google Scholar
  26. [Sh] Shimura, G.: Introduction to the arithmetic theory of, automorphic functions. Publ. Math. Soc. Japan, vol. 11) Tokyo: Iwanami Shoten 1971Google Scholar
  27. [T] Taylor, R.: On Galois representations associated to Hilbert modular forms. Invent. Math.98, 265–280 (1989)Google Scholar
  28. [W] Wiles, A.: On ordinary λ-adic representations associated to modular forms. Invent. Math.94, 529–573 (1988)Google Scholar

Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • Fred Diamond
    • 1
  • Richard Taylor
    • 2
  1. 1.Department of MathematicsColumbia UniversityNew YorkUSA
  2. 2.D.P.M.M.S.Cambridge UniversityCambridgeUK

Personalised recommendations